The most common radio frequency (RF) phase detector is a double balanced mixer. A double balanced mixer has a radio frequency (RF) port, a local oscillator (LO) port and an intermediate frequency (IF) port. The impedance of these three ports is 50 ohms. The mixer produces both a sum and a difference product. The sum product is removed by filtering so that only the difference product remains. The difference product for an ideal mixer is a cosine of the phase difference of the LO and RF frequencies. The phase slope of the mixer is a function of the IF power output. Because the derivative of a cosine wave is a sine wave, the peak voltage of the sinusoid is equal to the phase slope (volts/radian) when the output is at zero volts. For example, zero dBm at the IF output of the mixer is equal to a 0.316 volt peak sinewave into 50 ohms, and the phase slope is 0.316 volts per radian at zero volts output.
The IF power at the output is a function of the RF and LO power at the input and the conversion loss of the mixer. Conversion loss is the difference between the RF power and the IF power. Usually the LO power is much greater than the RF power, which gives the minimum conversion loss. The typical conversion loss of a mixer will vary between 6 and 9 dB. 3dB of the conversion loss is due to the lost power in the sum product that is filtered. The extra conversion loss is due to losses in the mixer and efficiency of the switching diodes. Increasing the RF power until it is equal to the LO power will increase the IF power and phase slope but at a lower conversion loss.
With equal power at the LO and RF ports, the output approaches a triangle wave instead of a cosine wave. In order to maintain a consistent definition of conversion loss of a phase detector, it can be redefined in terms of phase slope, IF port source resistance, RF power and RF source resistance. Let phase slope equal K.phi., IF source resistance equal R.sub.i, RF peak voltage equal V.sub.r, and RF source resistance equal R.sub.r. The conversion loss is: EQU (10)Log(V.sub.r.sup.2 /R.sub.r)-(10)Log(K.phi..sup.2 /R.sub.i)
Because K.phi. equals the peak IF voltage for a cosine IF output, this definition is consistent with the case where the RF power is much less than the LO power. The conversion loss for mixers where the RF and the LO power levels are equal is typically 12 to 15 dB. For example, a typical high level mixer with +20 dBm power into the RF and LO ports would have a peak RF voltage of 3.16 volts and a phase slope of 0.56 to 0.8 volts per radian.
By modeling the IF output of the mixer as an ideal voltage source and a 50 ohm source resistance, the noise floor of the phase detector can be determined. The source voltage is double the voltage measured when terminated into a 50 ohm load resistor because of the divide ratio of the source resistance and the load resistance. The single sideband phase noise of the phase detector referred back to the RF and LO source is equal to: EQU (10)Log(0.5(E.sub.n /K.phi.).sup.2),
where E.sub.n is the IF source resistance noise. Therefore, a typical mixer with a K.phi. of 0.5 volts per radian terminated in 50 ohms would have a source voltage of 1 volt per radian and a source noise of 0.89 nanovolts, giving a single sideband phase noise floor of -184 dBc in a 1 Hz bandwidth.
The noise figure of the phase detector is 3 dB less than the conversion loss of the phase detector as defined above. For the above example, a conversion loss of 14 dB and a RF power of 18 dBm would give the 0.5 volts per radian discussed. 18 dBm of RF power has a single sideband phase noise floor of -177-18=-195 dBc. The noise figure is -184-(-195)=11 dB. This result is 3 dB less than the 14 dB of conversion loss. The reason that the noise figure of the phase detector is 3 dB better than the conversion loss is that the double sideband noise at the RF port is converted to single sideband noise at the IF port. When relating single sideband noise at the IF port back to single sideband noise at the RF port, there is a 3 dB correction factor.
The amplifier that follows the phase detector will also contribute to the noise floor of the phase detector. Its contribution can be accounted for in terms of noise figure. The noise figure of a typical differential pair amplifier is about 3 dB for a 50 ohm source impedance. For the example above the total noise floor of the phase detector and amplifier following the phase detector will be -181 dBc in a 1 Hz bandwidth giving a total noise figure of 14 dB.
Another type of phase detector can be described as a sum-difference peak detector. This detector adds the RF to the LO at one output port and subtracts the RF from the LO at the other output port. By peak detecting the signals at the sum port and difference port and subtracting the outputs of the peak detectors, a very high phase slope for relatively low RF and LO powers is achieved. However, the source impedance of a peak detector can be very high. Given the definition of the conversion loss of the phase detector, a very high phase slope could have a very poor conversion loss if the IF source impedance is very high. For example, using a peak detector on the sum and difference ports would give an IF voltage output of equal to twice the RF voltage input. With a source impedance of about 10000 ohms, the conversion loss would be 17 dB. This high a conversion loss makes the phase detector undesirable for low noise applications.